Question: A composite function can be written as $w\bigl(u(x)\bigr)$, where $u$ and $w$ are basic functions. Is $g(x)=(2x^2+5x)\tan(x)$ a composite function? If so, what are the "inner" and "outer" functions? Choose 1 answer: Choose 1 answer: (Choice A) A $g$ is composite. The "inner" function is $2x^2+5x$ and the "outer" function is $\tan(x)$. (Choice B) B $g$ is composite. The "inner" function is $\tan(x)$ and the "outer" function is $2x^2+5x$. (Choice C) C $g$ is not a composite function.
Solution: Composite and combined functions A composite function is where we make the output from one function, in this case $u$, the input for another function, in this case $w$. We can also combine functions using arithmetic operations, but such a combination is not considered a composite function. Relationship between the functions Our $2$ functions appear to be $2x^2+5x$ and $\tan(x)$, but neither of them takes the other as its input. We combine the functions by multiplying them, not by composing them. Answer $g$ is not a composite function.